We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar (KRb)-K-40-Rb-87 molecules [1, 2]. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold K-40 and Rb-87 atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X-1 Sigma(+) and a(3)Sigma(+) vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally averaged transition dipole moment to the lowest rovibrational level of the X-1 Sigma(+) state. Finally, we obtained an estimate of the polarizability of the initial and final rovibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules.